@C.Marius: the crawls were not properly scheduled. After a full crawl, results started to appear in the web analytic webpart. You may answer to the question, I'll grant you the reward for the answer!
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Steve BApr 22 '13 at 19:38

That said, does it means I can use a search query to retrive the same results? I'll have to apply some visual customization and I bet this will be easier using a custom XSL transformation with search result webpart
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Steve BApr 23 '13 at 7:22

Not really as all the data is stored in database (default WSS_Logging).
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C. Marius - MVPApr 23 '13 at 13:08

Is Search service properly working (returning results) after a full crawl

With the job enabled and that some data in the database has been stored

If you tried to customize the Web Analytics reports I've also noticed that the "Claims to Windows Token Service" must be started. I've found somewhere on a blog that also UDF Assemblies via Excel Service Application must show the reference to Microsoft.Office.Server.WebAnalytics.UI assembly in GAC.

Sorry, but without any other details with regards to what you've tried already, it would be difficult to propose anything else.